1 + (2 + 3 * 4) + (5 + 6 * 7 + 8 * 9 * 10) +....+ nth term

// Problem: Get the sum of 1 + (2 + 3 * 4) + (5 + 6 * 7 + 8 * 9 * 10) + .... + nth term

/*
 * while n = 10, sum is 782
 * while n = 6, sum is 26
 * while n = 19, sum is 10123
 * while n = 2, sum is 3
 */

#include <iostream>
using namespace std;

int main() {
    int n; cout << "Input: "; cin >> n; // getting nth term
    int sum = 0, loop = 1 /*for first inner loop*/, num = 1 /*number initializtion*/;
    bool run = true; // to run the outer loop

    while (run) {
        int inner_sum = 0; // for taking the value of each closed bracket
        for (int x = 1; x <= loop; x++) /*inner loop for the sum of bracket*/ {
            int mult = 1;
            for (int y = 1; y <= x; y++) /*inner loop for product*/ {
                mult *= num;
                if (num == n) { // if num crosses n then stop multiplying
                    run = false;
                    break;
                }
                num++; // number increment by 1
            }
            inner_sum += mult; // sum of each product of a bracket
            if (num == n) // if num crosses n then stop next loop
                break;
        }
        sum += inner_sum; // sum of participated brackets
        loop++; // increment of repeatation of inner loop
    }
    cout << "\nSum: " << sum << endl;
    return 0;
}